Bell's inequality, generalized concurrence and entanglement in qubits

It is well known that the maximal violation of the Bell's inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an n-qubit state has not been found. In this paper, we demonstrate some extensions of the relation between the upper bound of the Bell's violation and a generalized concurrence in several n-qubit states. In particular, we show the upper bound of the Bell's violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell's violation.